Ballistic Coefficient

What a BC is

A ballistic coefficient (BC) is a sectional-density / form-factor ratio that scales a standard drag curve to a particular bullet:

Cd_bullet(M) = Cd_std(M) / BC_effective(M)

In lob Cd_std is one of the G* tables (Drag Functions); division by BC is performed in the spline coefficients so the solver sees a single Cd(M) lookup. BC_effective may be constant (single-BC mode) or a Mach-dependent curve built from multiple BC/velocity pairs (BC/Velocity-Band Transformation).

BCs are expressed as pounds-mass per square inch (Pmsi), i.e. the customary American unit. Internally source/calc.hpp computes ρ·π / (8·BC·144) with 144 = in²/ft²; the solver stores drag_coeff = ρ·π / 8 and divides BC into the spline drags[60] (see Context and Results and Point-Mass Model).

Standard curves

The six curves G1, G2, G5, G6, G7, G8 in source/tables.hpp are 87-point Mach 0–5 tables from BRL/JBM. Lob projects each onto 16 PCHIP knots (Cubic Hermite Splines) at compile time (source/splines.hpp). G1 is the flat-base spitzer and the library default (most common among casual users relying on default settings); G7 is the boattail match preferred for long-range rifle bullets. The builder parameter BCDragFunction selects the curve; the atmosphere reference (Army vs ICAO) adds the kArmyToIcaoBcConversionFactor (≈0.982) before the division.

Single BC

With BallisticCoefficientPsi(BC) the context stores

drags[i] = coefs_std[i] / (BC · conversion) (source/lob_builder.cpp)

A constant BC across all velocities reproduces the single-BC result exactly; the BC-band test BCVelocityBandsConstantBcScalesG1Curve (test/source/lob_builder_test.cpp) verifies this to 1e-4.

Why bands

A single BC cannot follow a bullet whose form factor changes with Mach (most modern bullets). Manufacturers increasingly publish BCs at several velocities. Fitting one Cd_std/BC curve through all of them by discretely switching BC would create a kink in Cd(M) and a discontinuity in the numerical derivative. Instead lob builds a smooth 1/BC(M) curve and multiplies it with Cd_std(M).

See BC/Velocity-Band Transformation for the full case study.